Elastic Moduli of materials chap 2 Flashcards
What is stress?
The effect of the force applied
sigma= force/ cross sectional area (base)
Benefits of using stress?
Same stress regardless of change in material in comparison with force
What is strain?
Deformation in response to applied force
- final length - original/ original length
Benefits of using strain?
Preferred to elongation as you can use regardless of material size or length
Young modulus curves
- relationship between stress and strain
Metals
- low strain levels = linear relationships
Ceramics
- linear relationship between stress and strain until sudden fracture
Shape memory alloy
NiTi
- has memory of original shape
- initially linear then deforms but deformation is reversible
Hooke’s law
- Relationship between stress and strain is linear when strain is small
- when the relationship is linear is when we are in the materials’ elastic regime and the form is recoverable
stress= materials property (E) times strain
Basic stress and strain states?
- definition
- Equation
- Tension(+) and Compression(-) stress and strain
- uniaxial tension = going out
- uniaxial compression = going in
- Equations
same as OG stress and strain resulting in Hooke’s law - Shear stress and strain
- stress - force over cross sectional area
- strain = tan theta
- Hooke’s law= shear stress = shear modulus x shear strain - Hydrostatic pressure (stress)
- signs are opposite to uniaxial
compression (+) (under the sea) and tension
(-) (on mountain)
- (dilation) = change in volume/ original volume
- Hooke’s law = hydrostatic pressure= negative bulk modulus x dilation
What are the complex stress and strain states?
- Biaxial tension and compression ( equilibrium force on all sides)
- Bending (tension on one side compression on next and middle strain neutral)- s-s are non uniform
- Torsion (rotating shaft)- pure shear
Equation :
shear strain = theta/ original length x r
shear stress = Gtheta/ original length x r
max will be times original radius
Poisson’s ratio?
relationship between lateral (diameter) strain and axial (length) strain
v cylinder = - lateral strain ( final diameter over original diameter for cylinder)/ axial strain ( final
length/ original length for cylinder)
v rectangle ba
strain x and strain y = lateral
strain z axial
strain x = strain y = negative Poisson’s ratio x strain z
What does Poisson’s ratio mean?
v= 0.5 little change in volume- iso-volume
v< 0.5 variation in volume
Isotropic/ ani-tropic
- isotropic = same behaviour in all directions of rotation
- ani-tropic = metals, plastics, wood
homogenous / heterogenous
= same behaviour when elongated or translated
= heterogenous = rocks
Effect of Elastic moduli ?
The higher the elastic moduli the less the material deforms Low E - vaulting poles - springs -cushions
High E
- bridge
What are the three primary types of interatomic bonding?
- Strong bonds (1000-4000K)
- Ionic
- covalent
- Metallic
What is ionic bonding?
- Non metal and metal
- non directional bonding = efficient packaging
- metallic easily give up their valence electrons to the non metallic
- in the process all atoms acquire a stable or inert gas configuration and an electrical configuration as they become ions
- High electron negativity
What is covalent bonding?
- non metals
- directional (specific packing)
- establish stable electron configurations by the sharing of electron
- similar EN
- ceramics: pottery, rocks, glass
- high melting point metals : W,Mo, Ta
- Polymers!!!- back bone of polymer chains
What is metallic bonding?
- in metals and their alloys
- bond between sea of delocalized electrons and positive metal ions
- non directional (packed tightly)
- freedom of movement
What is secondary interatomic bonding?
- weak bonds (100-500K)
- Van der Walls
- Hydrogen bonding
What is a dipole?
A moment where there is a separation between the positive and negative parts of an atom = electric dipole
Types of a dipole
- electrically symmetrical
- fluctuating
- induced
- permanent
What is Young’s modulus?
Measures how easily a material deforms or stretches
Small no= very elastic
Bonding force
Bonding force is the coulombic attraction or repulsion between two oppositely charged species.
When they’re a certain (r-separation) they begin to be attracted but they can’t get too close especially atoms as they negative electron clouds will start to repulse as they overlap.
Pulling apart atoms will be resisted by attractive force and compressing atoms will be resisted by repulsive/restrictive force
Behavior of force with relation to distance?
At big r, force is positive (attractive) and at small r force is negative (restrictive)
Bond Stiffness
The gradient of f-r curve is a measure of the bond stiffness at a certain point
Also directly correlates to Young’s modulus, as S increases, Young’s modulus increases
What is the order of strongest to weakest bonds?
ionic> covalent>metallic>hydrogen>Van der Walls
Draw out the shear schematic diagram
Draw the young modulus curve for metals, ceramic and polymers
Bond energy
Potential energy of the bond between two atoms
The trough in the UR curve indicates the strength of the interatomic bonds
Draw F-r curves for weak and strong materials
- assymetrical
gradient - bond stiffness- Young’s modulus
Draw U-r curves for strong and weak materials
- integral of FR
- assymertrical
- end of smiling face starting vertical
How does bonding force dictate a material’s properties?
- For polymers- strongs bonds within atoms (covalent bonds) but have weak bonds between chains (van der walls)- due to this weak bonds- a lot of free space, and not tight packing of atoms, and weak bonds in polymer materials allows for the greater ductility which they display
- For metals- metallic bonds- force of attraction between positive metal ion cores and sea of delocalised electrons, sea of delocalised electrons sheilds ion cores from repelling allowing for tighter packing and more dense materials leading to higher strength, stiffness and density but the electrons allow the layers of atoms to slide past each other which also makes metals ductile
- For ceramics bonding forces are ionic to covalent - because of the ionic bonding ( cations sharing electrons with anions), atoms cannot slide past each other, if tensile forces applied, ceramics immediately break at yeild point because the cations and anions are brought into contact and repel each other causing fracture
Coefficient of Thermal expansion (a1)
Solid expands when heated and contracts when cooled
coefficient of thermal expansion= rate of contraction and expansion
- a1 = change in strain T over change in T
strain T = change in length over og. length
when temperature increases, mean position of UR curves increases and shifts to left
path of mean position –> describes thermal expansion
slope of the mean distance curve defines a1
Melting
The collapse of a crystalline structure of atoms when atomic vibration due to increased temperature is strong enough
determined also by bond energy as well as the crystal structure
What is the effect of a materials’ Young modulus what does it tell us about the material?
What is the range of Young’s modulus for each class of material?
How do you work out the percent ionic character for ceramic materials?
- work it out for CaF2 , MgO, Sio2, SiC, Si3N4 and NaCl, Al203
Hydrogen bonding?
FON and H
Coloumbic forces between polar molecules such as HF,H20,NH3, due to the H at the end of atoms being attracted strongly to the negative ends of the molecule
- reason why some polar molecules have such high melting points
Draw the tetrahedron of bonding to understand the bonding present in the three classes of materials?
What are bonding forces?
The attractive or repulses forces between atoms, molecules or ions
How does bonding forces contribute to Young’s modulus?
- The slope of F-r curves = stiffness of the material = change in force over change in separation,
- young’s modulus is a measure of the stiffness of a material as it measures how easily a material deforms
- young’s modulus is also reflection of all the bonds that are actioned when stress is applied
Where are attractive and repulsive force at a majority
- Fa when r is large when there is pulling of atoms apart with r greater than equilibrium separation- above the x-axis
- Fr when there is r smaller than the equilibrium separation when atoms are being pulled together - below the x-axis
Stiffness and seperation
What is the equation for coloumbic force of attraction?
What is fmax
The highest point on the f-r curve
the theoretical maximum force a bond can endure
the theoretical strength of a material
the stronger the bonding the higher the fmax
What is the equation for bond energy
Aq1Q2/r
Relationship between thermal expansion, bond energy, melting temp
Higher the bond energy, smaller the thermal expansion co-efficient
the higher the bond energy, the stronger the bond, the lower the thermal expansion coefficient and the higher the melting temperature and the closer atoms are to each other- think of physical attraction- farther apart less strong attraction
What happens to a material under uniaxial tensile loading
- elongate in axial directions( length) and contract in lateral direction
What are the 4 elastic properties of a maerial? EGKv
E- Young’s modulus
G shear modulus
K Bulk’s modulus
v Poisson’s ratio
bonding type dictates
- electrical conductivity
- thermal conductivity
- chemical reactivity
bonding strength dictates
- elastic modulus
- melting temp
- theoretical strength
- thermal expansion coefficent
